I am in need of some serious homework help!

A high speed passenger test train travels from Columbia station to Penn station in exactly 8 hours. The distance traveled in miles from Columbia, at any given time in hours is given by the following function: s(t)=6t^3+72t^2.

A high speed passenger test train travels from Columbia station to Penn station in exactly 8 hours. The distance traveled in miles from Columbia, at any given time in hours is given by the following function: s(t)=6t^3+72t^2.

How many miles has the train traveled in 2 hour into the trip?

What is the distance in miles from Columbia station to Penn Station?

Hello,

sub in the given time into your equation:

a) t = 2 h. Therefore s(2) = 6*2^3+72*2^2 = 336 miles

b) The train needs 8 h for the complete travel. That means the distance between the two stations is s(8). Do as I've demonstrated in a). You should come up with 7680 miles. (Personal remark: I'm not very familiar with the geography of the United States, but this result looks as if the train zigzagged through all states on it's way from station to station)

Your Right this is an error. It should be a negative

A high speed passenger test train travels from Columbia station to Penn station in exactly 8 hours. The distance traveled in miles from Columbia, at any given time in hours is given by the following function:
s(t)= - 6t^3+72t^2.

A high speed passenger test train travels from Columbia station to Penn station in exactly 8 hours. The distance traveled in miles from Columbia, at any given time in hours is given by the following function:
s(t)= - 6t^3+72t^2.
How many miles has the train traveled in 2 hour into the trip?
What is the distance in miles from Columbia station to Penn Station?

Hello,

sub in the time t = 2 into your equation and you'll get:
s(2)=-6*(2)^3+72*(2)^2 = 240 miles

The complete journey takes 8 h. So plug in t = 8 into your equation to get the distance:
s(8) = -6*(8^3)+72(8)^2 = 1536 miles

By the way: This problem isn't much better than the first version because if the train travels 15 hours, it has travelled a distance of -4050 miles. That means it's going backward with a average speed of 270 miles / hour .